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   "source": [
    "# 第二次作业第3题\n",
    "作者：赵飞\n",
    "学号：202018019427078\n",
    "日期：2021-04-24"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 待插值数据点\n",
    "x = np.array([-1, 0, 2.0, 1.0])\n",
    "y = np.array([1.0, 0.3, -0.5, 0.8])\n",
    "plt.plot(x, y, '.', label=\"raw data\")\n",
    "# 插值加密点\n",
    "xnew = np.linspace(-3, 4, 100)\n",
    "for method in ['multiquadric', 'gaussian', 'linear']:\n",
    "    f = interpolate.Rbf(x, y, function=method)\n",
    "    ynew = f(xnew)\n",
    "    plt.plot(xnew, ynew, label=\"Rbf with \"+method+\" interpolation\", linewidth=0.5)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ]
}